MPA Shapes

We’ve come across a few MPA optimizations in the past. So far all the solutions were in terms of a single rectangle. For example we can ask the Bayesian optimizer to find the best rectangular MPA that maximizes profits over 20 years in a scenario where there are too many boats.
The shape depends on the biology, number of boats, etc. However for the scenario I ran this time we get this shape:

A more challenging question would be: if it could be any shape what MPA should we choose? Since the map is a grid, we could really be asking which cell of the map should be closed and which open. Given that the map is 50 by 50 we need to maximize a boolean vector of size 2500. This is quite hard to do with the Bayesian toolchain we got so I am using standard genetic algorithms for it. The result is plain weird:

Most of the map is protected but there aren’t areas of the sea completely sealed off. There is always a near permissable cell available for fishing.

The interesting result is that the weird MPA shapes increases profits compared to the best rectangle by about 80%. This is due of course to the higher number of free parameters. However this profits come at a cost in the sense that the optimizer found the MPA shape that allows the maximum extraction over 20 years.
At year 21 the weirdly shaped MPA world has almost no fish left, while the rectangle still has some.

In a way giving more freedom to the optimizer tends to accentuate its negative side. That is the literal optimization of score function at the expense of everything else.

Heterogeneity

Imagine we take the familiar heterogeneous fleet scenario where there are 50 big boats and 50 small boats. We want to maximize both the income of small fishers and the total landings. I changed some numbers here and there to make this slightly faster but we already know what happens if you can build MPA rectangles. Basically you can give up quite a lot of small income fishers to increase landings initially, but then you hit a flat area where you need to destroy small fishermen before you see any further improvement in landings.

What happens however if instead of rectangles we can build any shape we want? The result is that we can get a lot more landings. Strictly speaking rectangles are just a subset of the shapes so the new Pareto front ought to be strictly better. However here we hit the limits of the optimizer (NSGA here). Fundamentally it is really hard (at least over 20 generations) for it to figure out the idea of rectangles to cover small fishermen. The end result is that the new Pareto front is not as wide as it can be simply because the optimizer hasn’t figured that out.

This is a nice demonstration of the limits of simple maximization and therefore the need to manage the number of parameters to deal with (or just run the simulation for a lot longer).